Converting Numbers to and from scientific notation

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Vocabulary

Scientific notation is all about how to write large and small numbers  as multiples of 10.

If your exponent is

POSITIVE: move decimal point to the LEFT.

NEGATIVE: move decimal point to the RIGHT.

You would write scientific notation using the following format.

_significant figure_ x 10 ^—-power

Examples

Write 6998000000 in scientific notation

1. Count the number of significant figures (all the numbers that are not zeros). There are four significant figures. These are the numbers that you will include in your scientific notation expression.

6998000000

2. Move your decimal place to the left until you reach the first and second number in your figure. The decimal should be placed between these two numbers.

6.998000000

3. Rewrite your answer in scientific notation

6.998 x 10 ^9  (pronounced as “six point nine nine eight times ten to the ninth power”)

When you write your answer in standard notation, you are converting your scientific notation expression into its original form. Let’s look at the example above. In scientific notation, it is written as 6.998 x 10 ^9; however, in standard form the number is written as 6998000000.

Example

7.75 x 10 ^-1    = 77.5

Move your decimal place once to the right.

For the Millionth Time

You are an author of a new mathematics textbook. A publisher offers you a deal that you simply cannot refuse. Or can you? He gives you two options: 1) Reward you with a 10,000,000 lump sum of cash, or 2)Pay you in small increments of 1 cent per week with the promise of doubling your wages every week.

Write an equation to represent the number of cents being paid to you each week.

WEEK	PAYMENT (CENTS)	PATTERN	EXPONENTIAL REPRESENTATION
0	1	1 X 2	2^0
1	2	1 X 2 X 2	2^1
2	4	1 X 2 X 2 X 2	2^2
3	8	1 X 2 X 2 X 2 X 2	2^3
4	16	1 X 2 X 2 X 2 X 2 X 2	2^4
5	32	1 X 2 X 2 X 2 X 2 X 2 X 2	2^5
6	64	1 X 2 X 2 X 2 X 2 X 2 X 2 X 2	2^6
7	128	1 X 2 X 2 X 2 X 2 X 2 X 2 X 2 X 2	2^7
…	….
25	33,554,432

EQUATION: Y = 2 ^X

OBSERVATIONS

o   No constant slope- changes

o   Numbers only double if base is 2.

o   Positive base means function is positive

o   Negative exponents mean fraction